A former Obama administration official whose nomination to a powerful health care post was derailed by Senate Republicans said Tuesday that he is strongly considering a run for governor in 2014.

If he decides to run, Dr. Donald M. Berwick would follow a path charted by Elizabeth Warren, who began her term as senator this week, two years after her nomination to lead a federal consumer protection agency was shelved amid Republican opposition.

Berwick ran the Centers for Medicare & Medicaid Services and is one of the nation’s leading ­experts on health cost and quality. Obama installed him using a ­recess appointment in 2010, but Berwick resigned in late 2011 when Republicans made clear they would strongly oppose his confirmation. At the time, the height of the national debate over Obama’s health care overhaul, Republicans accused ­Berwick of wanting to ration services, a charge he called a mischaracterization.

Berwick, a Newton pediatrician and longtime Harvard faculty member whose wife is the chairwoman of the department of public utilities in the administration of Governor Deval ­Patrick, said he has been contemplating a run for the past two or three months, meeting with 40 or 50 people, including political veterans and consultants. He did not give a time frame for a final decision, but said it would be soon, after he meets with more people.

“I’m strongly considering it,” said Berwick, whose interest in the office was first reported by State House News Service.

While he would bring deep policy knowledge to a governor’s race, it is unknown whether Berwick can mount a serious candidacy, as a newcomer to politics who has never raised money or glad-handed voters at a strip mall.

His initial meetings included a chat with Patrick and his lieutenant governor, Timothy P. Murray, who is also weighing a run. Berwick said the 15- to 30-minute meeting with Murray in his State House office Monday was a courtesy call, as he knows that Murray, too, is eyeing the corner office.

Murray’s spokesman, Scott Ferson, said Murray appreciated the visit and told Berwick that a decision to seek office is a personal one.

State Treasurer Steve ­Grossman, who is also considering a run on the Democratic side, said he had not met with Berwick. But he praised his background and track record.

If Berwick were to emerge from a Democratic field, his nomination could create an ­interesting clash with Charles D. Baker, a Republican health care executive who is considering another run after his 2010 loss to Patrick. Baker did not ­respond to messages left Tuesday night.

Berwick said he has been asking three questions as he meets with key political players: Can he make a contribution? Does he stand a chance of winning? What is the job like?

“I’m very favorable about the answers I’ve been getting, but I’ve got a lot more to learn first,” Berwick said.

Berwick, 66, said that he ­began thinking about elected office when he was in Washington. He said that even as he was thrust into the national health care controversy, the good outweighed the negative.

“I saw problems,” he said. “I saw paralysis in the political combat at a level that is not serving the country well, and I began to think more and more about effective public service, effective government.”

He said his decades of health care experience offer him a broader window into the issues that matter to people, including education, public safety, and the economy.

“I get more and more excited about the idea of Massachusetts as a model,” he said. “I think the state is a terrific arena for progress in improving the human condition in a way that Washington is currently having trouble with because of the divisions and the rancor.”

Berwick’s outsider status could be viewed as an asset, given the state’s history of electing figures from outside Beacon Hill to lead the state, including Mitt Romney, William F. Weld, and Patrick.

“There could be another ­Deval Patrick out there,” said Philip W. Johnston, a former chairman of the state Democratic Party. “Maybe it’s Don Berwick.”

Also Tuesday, Dr. Joseph Avellone, a Harvard-educated surgeon and former Wellesley selectman, said in a phone inter­view that he has filed ­papers to seek the Democratic nomination for governor.

“I think that what the Common­wealth is going to need is a focus on building a new economy for the 21st century,” said Avellone, an executive at Waltham’s Parexel International Corp., a biotechnology services company. Avellone, 64, who previously was chief operating officer of Blue Cross Blue Shield of Massachusetts, said controlling health care costs will also be a key part of his platform.

He described himself as “a moderate, progrowth” Democrat who worked on the presidential campaigns of Edward M. Kennedy, Gary Hart, Paul Tsongas, and John F. Kerry. He said his experience in town government is an asset. “I know how to balance budgets in the public sector,” he said.

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